Part I Probability 1
Chapter 1 Basic Probability 3
Random Experiments
Sample Spaces
Events
The Concept of Probability
The Axioms of Probability
Some Important Theorems on Probability
Assignment of Probabilities
Conditional Probability
Theorems on Conditional Probability
Independent Events
Bayes' Theorem or Rule
Combinatorial Analysis
Fundamental Principle of Counting
Tree Diagrams
Permutations
Combinations
Binomial Coefficients
Stirling's Approximation to n!
Chapter 2 Random Variables and Probability Distributions 36
Random Variables
Discrete Probability Distributions
Distribution Functions for Random Variables
Distribution Functions for Discete Random Variables
Continuous Random Variables
Graphical Intepretations
Joint Distributions
Independent Random Variables
Change of Variables
Probability Distributions of Functions of Random Variables
Convolutions
Conditional Distributions
Applications to Geometric Probability
Chapter 3 Mathematical Expectation 78
Definition of Mathematical Expectation
Functions of Randem Variables
Some Theorems on Expectation
The Variance and Standard Deviation
Some Theorems on Variance
Standardized Random Variables
Moments
Moment Generating Functions
Some Theorems on Moment Generating Functions
Characteristics Functions
Variance for Joint Distributions
Covariance
Correlation Coefficient
Conditional Expectation, Variance, and Moments
Chebyshev's Inequality
Law of Large Numbers
Other Measures of Central Tendency
Percentiles
Other Measures of Dispersion
Skewness and Kurtosis
Chapter 4 Special Probability Distributions 113
The Binomial Distribution
Some Properties of the Binomial Distribution
The Law of Large Numbers for Bernoulli Trials
The Normal Distribution
Some Properties of the Normal Distribution
Relation Between Binomial and Normal Distributions
The Poisson Distribution
Some Properties of the Poisson Distribution
Relation Between the Binomial and Poisson Distribution
Relation Between the Poisson and Normal Distributions
The Central Limit Theorem
The Multinomial Distribution
The Hypergeometric Distribution
The Uniform Distribution
The Cauchy Distribution
The Gamma Distribution
The Beta Distribution
The Chi-Square Distribution
Student's t Distribution
The F Distribution
Relationships Among Chi-Square, t, and F Distributions
The Bivariate Normal Distribution
Miscellaneous Distributions
Part II Statistics 159
Chapter 5 Sampling Theory 161
Population and Sample
Statistical Interference
Sampling With and Without Replacement
Random Samples
Random Numbers
Population Parameters
Sample Statistics
Sampling Distributions
The Sample Mean
Sampling Distribution of Means
Sampling Distribution of Proportions
Sampling Distribution of Differences and Sums
The Sample Variance
Sampling Distribution of Variances
Case where Population Variance Is Unknown
Sampling Distribution of Ratios of Variances
Other Statistics
Frequency Distributions
Relative Frequency Distributions
Computation of Mean, Variance, and Moments for Grouped Data
Chapter 6 Estimation Theory 205
Unbiased Estimates and Efficient Estimates
Point Estimates and Interval Estimates
Reliability
Confidence Interval Estimates of Population Parameters
Confidence Intervals for Means
Confidence Intervals for Proportions
Confidence Intervals for Differences and Sums
Confidence Intervals for the Variance of a Normal Distribution
Confidence Intervals for Variance Ratios
Maximum Likelihood Estimates
Chapter 7 Tests of Hypotheses and Significance 224
Statistical Decisions
Statistical Hypotheses
Null Hypotheses
Tests of Hypotheses and Significance
Type I and Type II Errors
Level of Significance
Tests Involving the Normal Distribution
One-Tailed and Two-Tailed Tests
P Value
Special Tests of Significance for Large Samples
Special Tests of Significance for Small Samples
Relationship Between Estimation Theory and Hypothesis Testing
Operating Characteristic Curves
Power of a Test
Quality Control Charts
Fitting Theoretical Distributions to Sample Frequency Distributions
The Chi-Square Test for Goodness of Fit
Contingency Tables
Yates' Correction for Continuity
Coefficient of Contingency
Chapter 8 Curve Fitting, Regression, and Correlation 278
Curve Fitting
Regression
The Method of Least Squares
The Least-Squares Line
The Least-Squares Line in Terms of Sample Variances and Covariance
The Least-Squares Parabola
Multiple Regression
Standard Error of Estimate
The Linear Correlation Coefficient
Generalized Correlation Coefficient
Rank Correlation
Probability Interpretation of Regression
Probability Interpretation of Correlation
Sampling Theory of Regression
Sampling Theory of Correlation
Correlation and Dependence
Chapter 9 Analysis of Variance 328
The Purpose of Analysis of Variance
One-Way Classification or One-Factor Experiments
Total Variation
Variation Within Treatments
Variation Between Treatments
Shortcut Methods for Obtaining Variations
Linear Mathematical Model for Analysis of Variance
Expected Values of the Variations
Distributions of the Variations
The F Test for the Null Hypothesis of Equal Means
Analysis of Variance Tables
Modifications for Unequal Numbers of Observations
Two-Way Classification or Two-Factor Experiments
Notation for Two-Factor Experiments
Variations for Two-Factor Experiments
Analysis of Variance for Two-Factor Experiments
Two-Factor Experiments with Replication
Experimental Design
Chapter 10 Nonparametric Tests 363
Introduction
The Sign Test
The Mann-Whitney U Test
The Kruskal-Wallis H Test
The H Test Corrected for Ties
The Runs Test for Randomness
Further Applications of the Runs Test
Spearman's Rank Correlation
Appendix A Mathematical Topics 389
Appendix B Ordinates (y) of the Standard Normal Curve at z 392
Appendix C Areas under the Standard Normal Curve from 0 to z 393
Appendix D Percentile Values t[subscript p] for Student's t Distribution with v Degrees of Freedom 394
Appendix E Percentile Values [characters not reproducible] for the Chi-Square Distribution with v Degrees of Freedom 395
Appendix F 95th and 99th Percentile Values for the F Distribution with v[subscript 1], v[subscript 2] Degrees of Freedom 396
Appendix G Values of e[superscript - lambda] 398
Appendix H Random Numbers 399
Subject Index 401
Index for Solved Problems 407